importing (appending) materials from File
The downloaded files from that old site do not appear to be blend files, which is why appending does not work.

While there have been a few different material library addons, there are two options that are currently working (and included) with 2.80. The first addon is listed as Material Library and was previously called "matlib vx", the other is a new addon called BlenderKit which provides a much wider library of resources that includes models, scenes and brushes.